The Greece Historical Society got a grant to scan the early issues of The Greece Post. Those issues are now on NYS Historic Newspapers. There is this page with details on the newspaper and where you could just search that one paper. This was a Wolfe Publication and the first issue was dated April 27, 1967 (below). The last available online issue is July 8, 1986.

NYS Historic Newspapers is a great website that offers a lot of newspapers for free. From there main page you can search the whole website or click on a county and search just the one county. They currently have over 11 million newspaper pages available.